Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\ell^1$ Norm
Abstract
Targeting at sparse multi-task learning, we consider regularization models with an penalty on the coefficients of kernel functions. In order to provide a kernel method for this model, we construct a class of vector-valued reproducing kernel Banach spaces with the norm. The notion of multi-task admissible kernels is proposed so that the constructed spaces could have desirable properties including the crucial linear representer theorem. Such kernels are related to bounded Lebesgue constants of a kernel interpolation question. We study the Lebesgue constant of multi-task kernels and provide examples of admissible kernels. Furthermore, we present numerical experiments for both synthetic data and real-world benchmark data to demonstrate the advantages of the proposed construction and regularization models.
Cite
@article{arxiv.1901.01036,
title = {Multi-task Learning in Vector-valued Reproducing Kernel Banach Spaces with the $\ell^1$ Norm},
author = {Rongrong Lin and Guohui Song and Haizhang Zhang},
journal= {arXiv preprint arXiv:1901.01036},
year = {2019}
}